An arithmetic sequence is one in which each phrase grows by adding or removing a certain constant, k.
What is the arithmetic sequence?Given that each term has a common difference, this is an arithmetic sequence. In this instance, the next term is obtained by adding 13 to the preceding term in the series. To put it another way, a n = a 1 + d (n - 1) This is the arithmetic sequence's formula.
An arithmetic sequence is one in which each phrase grows by adding or removing a certain constant, k. In a geometric sequence, each term rises by dividing by or multiplying by a certain constant k.
A sequence of the form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence. The common difference of the sequence is d, and the number an is the first term. An = a + (n - 1)d gives the nth term of an arithmetic series.
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By using efficient water fixtures, the average American can cut water use to about 45 gallons of water per day. About how many gallons of water would the average American use in December if they used the new amount?
Answer:
45*31=1,395
that would be 1,395 gallons if water used in december.
Step-by-step explanation:
*image is attached*
Please help on this!!!!!
I’ll give Brainly
And points
(x,y) = (2,0) trust me substitution is easy
f(x)=8x-6 ; shifts 7 units right
The equation of the function is f'(x) = 8(x - 7) + 6
How to determine the equation of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 8x - 6
We have the transformation property to be"
shifts 7 units right
Mathematically, this can be represented as
f'(x) = f(x - 7)
So, we have
f'(x) = 8(x - 7) + 6
Hence, the function is f'(x) = 8(x - 7) + 6
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Liczba o 8 mniejsza od iloczynu liczb w i 3
Answer: 3w-8
Step-by-step explanation: I don't quite understand you because I speak English but it's 3w-8
Please help me with this question, will give brainliest.
To complete the two-column proof, the required statement and reason are explained below.
Properties of a parallelogram.A parallelogram is a given plane figure which has its opposite sides to be parallel and equal in length. It has its unique identifying properties.
Supplementary angles are two or more angles which add up to 180^o.
To complete the two-column proof, we have;
STATEMENT REASON
1. ABCD and GDEF are parallelograms Given
2. <C and <CDA are supplementary angles m<C + m<CDA = 180^o
3. m<C + m<F = 180^o Definition of supplementary angles
4. <EDG ≅ <F Definition of congruent angles
5. <EDG = <F Parallelogram opposite angles theorem
6. m<CDA = m<EDG Vertical angles congruence theorem
7. m<CDA ≅ m<EDG Definition of congruent angles
8. m<CDA ≅ m<F Given
9. m<C + m<CDA = m<C + m<EFG Substitution property of equality
10. <C and <F are supplementary angles Parallelogram consecutive
angles theorem
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what is 52.085 rounded to the nearest tenth
Answer:
52.1
Step-by-step explanation:
have great day!!!
Answer:
OK so
The 10th is the one right after the decimal. We are basically rounding that 0.
5 and above rounds up
below 5 rounds down
the next number is an 8,
so we would round it as
52.1
Step-by-step explanation:
Write six less than seven and one-half times the number of acres of land Joe has as an algebraic expression. Use a as your variable
An algebraic expression for six less than seven and one-half times the number of acres of land Joe has:
(7 1/2)a - 6
Let us assume that a represents the number of acres of land Joe has.
We need to write given statement as an algebraic expression.
Consider given statement.
Six less than seven and one-half times the number of acres of land Joe has.
i.e., six less than seven and one-half times 'a'
As we know six less than.. means Subtract 6 from ...
So, we rewrite above statement as,
subtract 6 from seven and one-half times 'a'
So, we get an expression (7 1/2 × a) - 6
We can write the mixed fraction seven and one-half times (7 1/2) as 15/2 (a proper fraction)
So, an algebraic expression becomes,
(15/2 × a) - 6
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Volume of a cone and cylinder
the volume of a cone will be 201.06 in³.
What is volume of cone?
The area or volume that a cone takes up is referred to as its volume. Cones are measured by their volume in cubic units such as cm3, m3, in3, etc. By rotating a triangle at any of its vertices, a cone can be created. A cone is a robust, spherical, three-dimensional geometric figure.. Its surface area is curved. The perpendicular height is measured from base to vertex. Right circular cones and oblique cones are two different types of cones. While the vertex of an oblique cone is not vertically above the center of the base, it is in the right circular cone where it is vertically above the base.
So the
V = (1/3)πr²h.
Given, data r = 5yards
h = 8 yards
Volume = 1/3 * π * r ²* h
V = 1/3 * π * 4 ²* 12 =201.06 in³.
Hence, the volume of a cone will be 201.06 in³.
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If you run at an average speed of 10 mi/h, how long will it take you to run 2.5 miles? (Write the answer with minutes at the end. e.g. 10 minutes)
It will take 15 minutes to run 2.5 miles at an average speed of 10 miles per hour.
What is Speed?speed is described as. the pace at which an object's location changes in any direction. Speed is defined as the distance traveled divided by the travel time. Speed is a scalar quantity because it just has a direction and no magnitude.
Given, you run at an average speed of 10 mi/h.
Since,
Average speed = 10 mi/h
or in minutes
Average speed = 10/60 = 1/6 miles per minutes
Thus,
to run 2.5 miles it will take:
time = distance/ speed
time taken to run 2.5 miles = 2.5 * 6 =15 minutes
therefore, to run 2.5 miles at the average speed of 10mi/h it will take 15 minutes.
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Please write word answer that I can use
The type of triangle that Kevin drew based on the information is a scalene triangle.
What is a scalene triangle?A scalene triangle is a triangle with different lengths for each of its three sides and different measures for each of its three angles. A scalene triangle's angles adhere to the angle sum property and always add up to 180 degrees.
A scalene triangle has three sides, each of which is measured differently. Each of a triangle's three interior angles has a different measurement. Scalene triangles don't have a symmetry line.
In this case, the sides are all different as illustrated in Kevin's case.
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What is the length of BC?
Using the concept of proportions and similar triangle theorem, the value of BC is x + [(x² + 3x) / 3x - 8]
What is Similar Triangle TheoremA similar triangle is a triangle that has the same shape as another triangle, but not necessarily the same size. Two triangles are similar if and only if their corresponding angles are equal and the ratios of their corresponding sides are equal.
The Similar Triangles Theorem states that if two triangles have corresponding angles that are congruent, then their corresponding sides are in proportion. In other words, if two triangles have the same shape, the ratio of any pair of corresponding sides is always the same.
To find the value of BC, we can use similar triangle theorem as;
AB / BC = DE / EC
Substituting the values;
4x - 6 / (x + EC) = x + 2 / EC
NB: BE = EC
4x EC - 6EC - x EC - 2EC = x² + 2x
NB: This is done after cross multiplying and collecting like terms
3x EC - 8 EC = x² + 2x
(3x - 8) EC = x² + 3x
EC = x² + 3x / 3x - 8
The length of BC = BE + EC
BC = x + [(x² + 3x) / 3x - 8]
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find the values of x and y in the parallelogram
The value of x is 4 and the value of y is 13 in the parallelogram.
What is a parallelogram?
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.
According to the properties of a parallelogram the opposing sides are equal and parallel.
AB = CD
So, the equation will be -
10 = y - 3
y = 10 + 3
y = 13
Now, another property of a parallelogram suggests that adjacent angles of a parallelogram equals 180°.
∠B + ∠C = 180°
So, the equation will be -
112° + ∠C = 180°
∠C = 180° - 112°
∠C = 68°
The opposite angles of a parallelogram are equal -
∠C = ∠A
So, the equation will be -
68° = 17x°
x = 68/17
x = 4
Therefore, the values of x and y are 13 and 4 respectively.
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please answer this its a maths question attached below this task
My answer's in screenshot format since Brainly bot is suspicious of long answers:
An angle measures 28° more than the measure of its supplementary angle. What is the measure of each angle?
The measure of each angle is 104° and 76°.
What are Supplementary Angles?Supplementary refers to angles that come together to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles. If two angles Supplementary one another if,
It has an acute angle on one side and an obtuse angle on the other.
The angles are both right angles.
Given An angle that measures 28° more than the measure of its supplementary angle,
let the angle be x
and supplementary angle of x = 180 - x
according to condition
x = 28 + 180 - x
2x = 208
x = 208/2
x = 104°
and supplementary angle of x = 180 - x
supplementary angle of x = 180 - 104
supplementary angle of x = 76°
Hence the angles are 104° and 76°.
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f(1)= 10 and f(21)= 2 ; find f(14)
the function value f(14) = 4.8.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function if one were mapped to a single value instead. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
f(1)= 10
f(21)= 2
Let the function f(x) = ax+b
f(1)= 10 = a+b
f(21)= 2 = 21a +b
20a = -8
a=-8/20
b = 208/20
f(14) = 14*(-8/20)+208/20 = 4.8
Hence the function value f(14) = 4.8.
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Estimate the sum
1.) 6.34
+ 9. 112
2.) 12.04
+. 10. 824
Estimate the difference
1.)8.5
- 3. 87
2.) 83. 55
-. 24. 37
Answer:
Sum
1:15.452
2:22.864
Difference
3:4.63
4:59.18
prove that any nonzero rational number may be written as the product of two irrational numbers.
If r is a nonzero rational number, then r is a product of two irrational numbers.
If q≠0 is rational and y is irrational, then qy is irrational.
: You know that if G
is a group and H≠G
is one of its subgroups then h∈H
and y∈G∖H
implies that hy∈G∖H
Proof: suppose hy∈H
You know that h−1∈H, and therefore y=h−1(hy)∈H
Contradiction
In our case, we have the group (R∗,⋅) and its proper subgroup (Q∗,⋅). By the arguments above q∈Q∗ and y∈R∖Q implies qy∈R∖Q
.
Simply multiply it by the square root of two to obtain an irrational number. A product of two irrational numbers, your original number is obtained by multiplying this irrational number by the square root of two, which is itself irrational.
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You bake 53 lemon cupcakes to take to a homeless shelter. If you keep 2 lemon cupcakes at home, how many boxes of 3 lemon cupcakes do you have to give away
Answer: 17 boxes
Step-by-step explanation: 53-2=51 (subtract 2 from 53 as they are left at home)
51/3=17 ( divide by 3 as one box contains 3 lemon cupcakes)
so the answer is 17 boxes
Problem 1 What is meant by the term 'Decision Analysis'? - Decision Analysis: The term decision analysis originated in 1964 by ROnald A. Howard, professor of Management Science and Engineering at Stanford University. - The objective of a decision analysis is to choose the most advantageous alternative from various alternative solutions of decision problems. - Decision analysis is systematic, quantitative and visual approach to addressing and evaluating important choices confronted by businesses. - Systematic approach means creating a constructive environment, investigating the situation, generating good solutions or alternatives, choosing the best solution and taking action. - Quantitative approach means to convert the problem into a mathematical model or formula to find the best solution. By using common quantitative tools. Decision tree, payback analysis and simulation. - Visual approach means to convert the problem into graphical charts to find the best solution.
Decision Analysis is a mathematical method for making decisions in uncertain environment.
What is environment ?
Environment refers to the surrounding conditions, resources and factors that can have an impact on an organism, community, or system. This can include physical factors such as weather, terrain, and pollution, as well as biological factors such as other living organisms, and social or economic factors such as culture, laws and economic conditions.
The process of Decision Analysis can be broken down into several steps:
1) Define the decision problem: Clearly state the problem and the decision maker's objectives.
2) Identify the decision alternatives: List all the feasible options available to the decision maker.
3) Specify the probability distribution of the uncertain parameters: Assign probabilities to the possible outcomes of the uncertain parameters.
4) Evaluate the expected value or expected loss for each alternative: Compute the expected value or expected loss for each alternative, using the probability distribution of the uncertain parameters.
5) Choose the alternative with the highest expected value or the lowest expected loss: Select the alternative that maximizes the expected value or minimizes the expected loss.
6) Sensitivity analysis: Check the robustness of the decision by studying the effect of small changes in the model's assumptions.
Decision Analysis is a mathematical method for making decisions in uncertain environment.
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A chef preheats an oven. It starts at room temperature, 68°F, and heats up 23°F per minute. How long does it take for the oven temperature to reach 275°F?
Please help me.
====================================================
Explanation:
x = number of minutes
y = temperature
The equation is
y = 23x+68
The slope 23 tells us how fast the oven is heating up. The 68 is the y intercept, and it's the starting temperature (when x = 0).
We want to find the value of x when y = 275
y = 23x+68
275 = 23x+68
275-68 = 23x
207 = 23x
23x = 207
x = 207/23
x = 9
It takes 9 minutes for the oven to reach a temperature of 275°F
--------
Check:
y = 23x+68
y = 23*9+68
y = 207+68
y = 275
The answer is confirmed.
COMBINING LIKE TERMS
9 + 6f - 7
Answer:
6f + 2
Step-by-step explanation:
The 9 and the - 7 are "like terms"
They are both constants. That is, they don't have a variable. The terms will be considered "like terms" if they have the same variables to the same power.
So we can combine 9 and - 7.
9 + - 7 is 2.
9 + 6f - 7
= 6f + 9 - 7
= 6f + 2
What is the answer for 7 to the power of zero?
No matter what the number is, the answer when raised to the power of zero is always 1.
No matter what the number is, the answer when raised to the power of zero is always 1
7 to the power of zero is written as 7^0.
The answer is 1, since any number raised to the power of zero is equal to 1.
Any number raised to the power of zero is equal to 1. This is true regardless of the number. For example, 7 to the power of 0 is written as 7^0. The answer is 1. This can be seen from the equation 7^0 = 7 x 1 = 1. Similarly, 8^0 = 8 x 1 = 1, and 9^0 = 9 x 1 = 1. This concept can be applied to any number, positive, negative, whole, fractional, or decimal. No matter what the number is, the answer when raised to the power of zero is always 1.
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& Ms. Patterson bought a case of pencils at the beginning of the school year.
• The case had 48 boxes with 24 pencils in each box.
She wants to give & pencils to each of her 23 students to begin the year.
How many extra pencils will she have after she gives the pencils to her students?
9
B
D
1.152
968
Answer: 968 extra pencils
Step-by-step explanation:
What is the HCF of 12 and 18 and 48?
The Highest Common Factor (HCF) of 12, 18, and 48 is 6. This means that 6 is the greatest number that can be evenly divided into all three numbers without leaving a remainder.
1. List out the factors of each number:
12: 1, 2, 3, 4, 6, 12
18: 1, 2, 3, 6, 9, 18
48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
2. Find the common factors of all three numbers:
1, 2, 3, 6
3. The greatest number of these common factors is 6, so 6 is the HCF of 12, 18, and 48.
The Highest Common Factor (HCF) is the greatest number that can be evenly divided into all the numbers in a set. To find the HCF of a set of numbers, we must first list out the factors for each number. The factors are the numbers that can be evenly divided into the original number. For instance, 1, 2, 3, 4, 6, and 12 are the factors of 12. We then compare the lists of factors of all the numbers and find the common factors. The greatest number of these common factors is the HCF. For example, the HCF of 12, 18, and 48 is 6, because 6 is the greatest number that can be evenly divided into all three numbers without leaving a remainder
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Point
(-3,5),
Line
x+6=0
Equation of line passing through the point and having slope m=1
y=mx+C
In this question, m=tan45°=1
So the equation becomes y=x+C
New line passes through (3,5)
Putting the values in the equation,5=3+c
C=2
New equation of line becomes y=x+2
Another line x+y−6=0
These two lines intersect at Q
y=x+2
y=−x+6
2y=8
y=4
Put the value of y=4 in line equation,
y=x+2
x=2
Q(2,4)
P(3,5)
O(0,0)
Distance between two points
=9×PQ² +14×O ² +10×OQ²
=9×2+14×34+10×20
=18+476+200
=694
What is slope?The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.The slope of any line can be calculated using any two distinct points lying on the line. The slope of a line formula calculates the ratio of the "vertical change" to the "horizontal change" between two distinct points on a line. In this article, we will understand the method to find the slope and its applications.The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.
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I got stuck, does anyone know how to do this?
Nothing can be done to this it is in its simplest form.
For what value of k has real and equal roots?
For [tex]$\mathrm{k}=2$[/tex] and[tex]$\mathrm{k}=-\frac{10}{9}$[/tex]given equation will have real and equal roots.
What are real and equal roots?If D=0, a quadratic equation has two roots that are equal. D (discriminant) = 0 b24ac=0 is required for a quadratic equation to have equal roots.If the discriminant of a quadratic equation is 0, then its roots are equal. A quadratic equation has equal roots if both of these roots are equal to the derivative's root. A quadratic function has no real roots and does not intersect the x-axis if the discriminant of the function is less than zeroOn comparing given equation with [tex]$\mathrm{ax}^2+\mathrm{bx}+\mathrm{c}=0$[/tex]we get,[tex]$a=1, b=-2(1+3 \mathrm{k})$[/tex] and [tex]$c=7(3+2 \mathrm{k})$[/tex]
For the roots to be real and equation D must be equal to zero,
[tex]\mathrm{D} & =\mathrm{b}^2-4 \mathrm{ac} \\[/tex]
[tex]0 & =4(1+3 \mathrm{k})^2-4 \times[7(3+2 \mathrm{k})] \\[/tex]
[tex]& =9 \mathrm{k}^2+6 \mathrm{k}+1-21-14 \mathrm{k} \\[/tex]
[tex]9 \mathrm{k}^2-8 \mathrm{k}-20 & =0[/tex]
The given equation will have equal roots, if
[tex]9 k^2-8 k-20 & =0 \\[/tex]
[tex](k-2)(9 k+10) & =0 \\[/tex]
[tex]k-2=0 \text[/tex] and [tex]9 k+10 & =0 \\[/tex]
[tex]k=2 \text[/tex] and [tex]k & =-\frac{10}{9}[/tex]
Hence, for [tex]$\mathrm{k}=2$[/tex] and[tex]$\mathrm{k}=-\frac{10}{9}$[/tex]given equation will have real and equal roots.
The complete question is,
Find the values of [tex]$\mathrm{k}$[/tex] for which the given equation has real and equal roots
[tex]$$\mathrm{x}^2-2 \mathrm{x}(1+3 \mathrm{k})+7(3+2 \mathrm{k})=0$$[/tex]
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Is 3 a an algebraic expression?
No, 3 is not an algebraic expression.
In mathematics, an algebraic expression is a combination of numbers, variables and arithmetic operations (such as addition, subtraction, multiplication and division) that can be evaluated to a specific value when the variables are assigned specific numerical values.
For example, 3x + 2 is an algebraic expression. Here, x is the variable and 3, 2 are constants. We can substitute any numerical value for x and evaluate the expression for that specific value.
On the other hand, 3 is a numerical value, not an expression. It doesn't contain any variables or operators that can be evaluated for different values. It is a constant value, it doesn't change with the change of x or any other variable.
In summary, an algebraic expression is a combination of numbers, variables and arithmetic operations, whereas 3 is just a numerical value, not an algebraic expression.
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UNIT-6 (QUESTIONS 4-5) POSTED THE REST PLS CHECK IT OUT.
Answer:
See below
Step-by-step explanation:
Domain refers to the x values of a function
Range refers to the y values of a function
HELP!
im doing a state test and i forget exactly how to solve these, and i cant get it wrong
Answer:
46cm
Step-by-step explanation: